The present invention relates to the field of image correlators.
None of the various modifications and improvements of the first photorefractive correlator described in Appl. Phy. Letts 37, 5-7 (1980) have performed as well as the phase-only filter (POF) correlator in terms of peak-to-noise ratio (PNR) and discrimination ability. In accordance with the present invention we present the first photorefractive two-beam coupling joint transform correlator (TBJTC). Furthermore, it is the first nonlinear JTC which operates via the compressional rather than the thresholding principle. Our simulations show that using compression in the hard-clipping limit, the TBJTC outperforms the POF correlator in regard to both SNR (signal-to-noise ratio) and PNR in both noise-free and cluttered environments. To our knowledge, this nonlinear TBJTC is the first implementation of an all-optical nonlinear JTC, requiring neither a spatial light modulator nor intermediate digital processing in the Fourier plane as called for by U.S. Pat. No. 5,119,443 to Javidi and Horner. Moreover, this is the first time that photorefractivity has been used in correlation using purely the phase information.
The classical joint transform correlator (CJTC) requires quadratic processor image sensor in the Fourier transform plane and performs equivalently to a classical matched filter (CMF) optical correlator. Such a correlator may be achieved by using a photorefractive square law detector. Although this filter detects signals in additive Gaussian noise it is well-known that it fails to detect objects in clutter noise. It is possible, however, to improve the discrimination ability, peak-to-noise and peak-to-sidelobe ratios of the CJTC by adding additional nonlinearities in the Fourier plane to increase the weight of the higher spatial frequencies in the signal. A square root nonlinearity applied to the intensity in the Fourier transform plane behaves like a phase-only filter correlator and hard clipping causes it to behave like an inverse filter correlator for noise-free inputs. We show here that energy transfer in photorefractive two-beam coupling provides nonlinear intensity conversion ranging from a square-law to a hard-clipped nonlinearity as the beam ratio increases.
In our experiment we used the light at the joint Fourier transform plane to amplify a weak uniform reference beam in barium titanate. In the diffusion limit of the photorefractive effect, two-beam coupling amplification of a uniform beam by a signal-bearing beam produces an amplified beam bearing a hard-limited quadratically filtered version of the signal beam. Moreover, the high diffraction efficiencies available with barium titanate provide a large dynamic range in the saturation nonlinearity. Our experimental results for simple inputs are supported by two types of computer simulations: an idealized plane wave model and a diffractive beam propagation model. In addition, our simulation using the idealized plane wave model for cluttered images demonstrated SNR performance comparable to the digital nonlinear JTC.